Journal article

FROBENIUS CIRCULANT GRAPHS OF VALENCY FOUR

Alison Thomson, Sawing Zhou

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | CAMBRIDGE UNIV PRESS | Published : 2008

Abstract

A first kind Frobenius graph is a Cayley graph Cay(K,S) on the Frobenius kernel of a Frobenius group $K \rtimes H$ such that S=a H for some a∈K with 〈aH〉=K, where H is of even order or a is an involution. It is known that such graphs admit 'perfect' routing and gossiping schemes. A circulant graph is a Cayley graph on a cyclic group of order at least three. Since circulant graphs are widely used as models for interconnection networks, it is thus highly desirable to characterize those which are Frobenius of the first kind. In this paper we first give such a characterization for connected 4-valent circulant graphs, and then describe optimal routing and gossiping schemes for those which..

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University of Melbourne Researchers